Edit Profile Quarteroni, Alfio M. Compute Distance To: Compute Author ID: quarteroni.alfio-m Published as: Quarteroni, A.; Quarteroni, Alfio; Quarteroni, Alfio M.; Quarteroni, Alfio. External Links: MGP · Wikidata · dblp · GND Documents Indexed: 341 Publications since 1979, including 58 Books Biographic References: 1 Publication all top 5 Co-Authors 45 single-authored 36 Saleri, Fausto 32 Rozza, Gianluigi 28 Gervasio, Paola 23 Dede, Luca 22 Manzoni, Andrea 19 Canuto, Claudio 19 Deparis, Simone 15 Veneziani, Alessandro 13 Discacciati, Marco 13 Valli, Alberto 12 Formaggia, Luca 11 Sacco, Riccardo 10 Lassila, Toni 9 Chen, Peng 9 Ruiz-Baier, Ricardo 8 Antonietti, Paola Francesca 8 Maday, Yvon 7 Agoshkov, Valeriĭ Ivanovich 7 Mazzieri, Ilario 7 Sacchi Landriani, Giovanni 6 Miglio, Edie 6 Nobile, Fabio 6 Parolini, Nicola 5 Ambrosi, Davide 5 D’Angelo, Carlo 5 Forti, Davide 5 Quaini, Annalisa 5 Vergara, Christian 4 Bartezzaghi, Andrea 4 Blanco, Pablo Javier 4 Dal Santo, Niccolò 4 Gastaldi, Fabio 4 Hussaini, M. Yousuff 4 Maggio, Fabio 4 Marini, Luisa Donatella 4 Pasquarelli, Franco 4 Zampieri, Elena 4 Zang, Thomas A. jun. 3 Badia, Santiago 3 Benner, Peter 3 Carlenzoli, Claudio 3 Crosetto, Paolo 3 Fatone, Lorella 3 Grandperrin, Gwenol 3 Grivet-Talocia, Stefano 3 Lions, Pierre-Louis 3 Malossi, A. Cristiano I. 3 Negri, Federico 3 Rossi, Simone 3 Schilders, Wilhelmus H. A. 3 Silveira, Luís Miguel 3 Tagliabue, Anna 2 Astorino, Matteo 2 Ballarin, Francesco 2 Bressan, Nicoletta 2 Brezzi, Franco 2 Burman, Erik 2 Colciago, Claudia Maria 2 Deville, Michel O. 2 Ferroni, Alberto 2 Filippi, Simonetta 2 Fourestey, Gilles 2 Gaudio, Loredana 2 Gerbeau, Jean-Frédéric 2 Gerbi, Antonello 2 Gizzi, Alessio 2 Iapichino, Laura 2 Laadhari, Aymen 2 Lions, Jacques-Louis 2 Massimi, Paolo 2 Micheletti, Stefano 2 Milišić, Vuk 2 Pacciarini, Paolo 2 Pagani, Stefano 2 Pegolotti, Luca 2 Quinodoz, Samuel 2 Rapetti, Francesca 2 Sala, Marzio 2 Salsa, Sandro 2 Scrofani, G. 2 Sequeira, Adélia 2 Stamm, Benjamin 2 Taddei, Tommaso 2 Tagliani, Aldo 2 Zhu, Shengfeng 2 Zunino, Paolo 1 Alonso Rodríguez, Ana 1 Altinakar, Mustafa Siddik 1 Andreianov, Boris 1 Arioli, Gianni 1 Ayuso de Dios, Blanca 1 Azaiez, Mohamed Naceur 1 Badea, Lori 1 Baroli, Davide 1 Battarra, Viliam 1 Becerra-Sagredo, Julián-Tercero 1 Beirão da Veiga, Hugo 1 Bendahmane, Mostafa 1 Benzi, Michele 1 Bonnemain, Jean ...and 98 more Co-Authors all top 5 Serials 34 Computer Methods in Applied Mechanics and Engineering 16 SIAM Journal on Numerical Analysis 14 Unitext 12 Journal of Computational Physics 12 Numerische Mathematik 10 SIAM Journal on Scientific Computing 9 Journal of Scientific Computing 8 Computing and Visualization in Science 7 Computers and Fluids 7 Calcolo 7 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 7 MS&A. Modeling, Simulation and Applications 6 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 4 Texts in Computational Science and Engineering 3 Computers & Mathematics with Applications 3 International Journal for Numerical Methods in Engineering 3 Applied Numerical Mathematics 3 Computational Mechanics 3 East-West Journal of Numerical Mathematics 3 Multiscale Modeling & Simulation 3 SIAM/ASA Journal on Uncertainty Quantification 2 International Journal for Numerical Methods in Fluids 2 Journal of Engineering Mathematics 2 RAIRO. Analyse Numérique 2 Surveys on Mathematics for Industry 2 Notices of the American Mathematical Society 2 European Journal of Mechanics. A. Solids 2 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 2 Springer Series in Computational Mathematics 2 Texts in Applied Mathematics 2 Bollettino dell’Unione Matematica Italiana. Series IX 2 International Journal for Numerical Methods in Biomedical Engineering 2 S\(\vec{\text{e}}\)MA Journal 2 Mathematics in Engineering 1 Applicable Analysis 1 IMA Journal of Numerical Analysis 1 Mathematical Methods in the Applied Sciences 1 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 1 Mathematics of Computation 1 Journal of Approximation Theory 1 Journal of Computational and Applied Mathematics 1 Mathematics and Computers in Simulation 1 SIAM Journal on Control and Optimization 1 Rendiconti del Seminario Matematico 1 SIAM Journal on Scientific and Statistical Computing 1 Statistics & Probability Letters 1 Chinese Annals of Mathematics. Series B 1 Mitteilungen der Gesellschaft für Angewandte Mathematik und Mechanik 1 Journal of Computational Mathematics 1 Parallel Computing 1 RAIRO. Modélisation Mathématique et Analyse Numérique 1 Japan Journal of Applied Mathematics 1 Numerical Methods for Partial Differential Equations 1 Numerical Algorithms 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 SIAM Journal on Applied Mathematics 1 Comptes Rendus de l’Académie des Sciences. Série I 1 Bollettino della Unione Matemàtica Italiana. Serie VII. A 1 Russian Journal of Numerical Analysis and Mathematical Modelling 1 Advances in Computational Mathematics 1 Vietnam Journal of Mathematics 1 Chaos 1 Revista Matemática Complutense 1 Journal of Mathematical Fluid Mechanics 1 Bollettino della Unione Matematica Italiana. Serie VIII. Sezione A. La Matematica nella Società e nella Cultura 1 Computational Methods in Applied Mathematics 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 AMRX. Applied Mathematics Research eXpress 1 Milan Journal of Mathematics 1 Mathematical Medicine and Biology 1 Mediterranean Journal of Mathematics 1 Acta Numerica 1 Bollettino della Unione Matematica Italiana. Series V. B 1 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Série A 1 Rendiconti del Seminario Matematico. Universitá e Politecnico di Torino 1 Contemporary Mathematics 1 Lecture Notes in Mathematics 1 Cambridge Monographs on Applied and Computational Mathematics 1 Networks and Heterogeneous Media 1 Discrete and Continuous Dynamical Systems. Series S 1 Journal of Mathematics in Industry 1 Communications in Applied and Industrial Mathematics 1 Boletín de la Sociedad Española de Matemática Aplicada. S\(\vec{\text{e}}\)MA 1 Lettera Matematica. International Edition 1 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings and Surveys 1 Monografías de la Real Academía de Ciencias Exactas, Físicas, Químicas y Naturales de Zaragoza 1 Annals of Mathematical Sciences and Applications 1 Numerical Mathematics and Scientific Computation 1 Communications on Applied Mathematics and Computation 1 Springer-Lehrbuch all top 5 Fields 238 Numerical analysis (65-XX) 145 Fluid mechanics (76-XX) 140 Partial differential equations (35-XX) 62 Biology and other natural sciences (92-XX) 55 Mechanics of deformable solids (74-XX) 22 General and overarching topics; collections (00-XX) 20 Calculus of variations and optimal control; optimization (49-XX) 19 Approximations and expansions (41-XX) 17 Ordinary differential equations (34-XX) 13 Linear and multilinear algebra; matrix theory (15-XX) 13 Computer science (68-XX) 11 Field theory and polynomials (12-XX) 9 Probability theory and stochastic processes (60-XX) 9 Geophysics (86-XX) 8 Optics, electromagnetic theory (78-XX) 8 Systems theory; control (93-XX) 4 Classical thermodynamics, heat transfer (80-XX) 3 Potential theory (31-XX) 1 History and biography (01-XX) 1 Combinatorics (05-XX) 1 Special functions (33-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Operator theory (47-XX) 1 Differential geometry (53-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Statistics (62-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Operations research, mathematical programming (90-XX) 1 Information and communication theory, circuits (94-XX) 1 Mathematics education (97-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH 273 Publications have been cited 8,382 times in 5,634 Documents Cited by ▼ Year ▼ Spectral methods in fluid dynamics. Zbl 0658.76001Canuto, Claudio; Hussaini, M. Yousuff; Quarteroni, Alfio; Zang, Thomas A. 1,302 1988 Spectral methods. Fundamentals in single domains. Zbl 1093.76002Canuto, Claudio; Hussaini, M. Yousuff; Quarteroni, Alfio; Zang, Thomas A. 713 2006 Numerical approximation of partial differential equations. Zbl 0803.65088Quarteroni, Alfio; Valli, Alberto 517 1994 Domain decomposition methods for partial differential equations. Zbl 0931.65118Quarteroni, Alfio; Valli, Alberto 495 1999 Spectral methods in fluid dynamics. 2nd corr. printing. Zbl 0717.76004Canuto, Claudio; Hussaini, M. Yousuff; Quarteroni, Alfio; Zang, Thomas A. 311 1991 Spectral methods. Evolution to complex geometries and applications to fluid dynamics. Zbl 1121.76001Canuto, Claudio; Hussaini, M. Yousuff; Quarteroni, Alfio; Zang, Thomas A. 208 2007 Numerical approximation of partial differential equations. 1st softcover printing. Zbl 1151.65339Quarteroni, Alfio; Valli, Alberto 190 2008 Approximation results for orthogonal polynomials in Sobolev spaces. Zbl 0567.41008Canuto, C.; Quarteroni, A. 168 1982 Numerical solution of the Navier-Stokes equations for viscous compressible flows. Zbl 0852.76051Carlenzoli, C.; Quarteroni, A.; Valli, A. 162 1994 Mathematical and numerical models for coupling surface and groundwater flows. Zbl 1023.76048Discacciati, Marco; Miglio, Edie; Quarteroni, Alfio 157 2002 Numerical mathematics. Zbl 0957.65001Quarteroni, Alfio; Sacco, Riccardo; Saleri, Fausto 146 2000 On the coupling of 3D and 1D Navier-Stokes equations for flow problems in compliant vessels. Zbl 1007.74035Formaggia, L.; Gerbeau, J. F.; Nobile, F.; Quarteroni, A. 141 2001 Reduced basis methods for partial differential equations. An introduction. Zbl 1337.65113Quarteroni, Alfio; Manzoni, Andrea; Negri, Federico 140 2016 Numerical mathematics. 2nd ed. Zbl 1136.65001Quarteroni, Alfio; Sacco, Riccardo; Saleri, Fausto 119 2007 Computational vascular fluid dynamics: problems, models and methods. Zbl 1096.76042Quarteroni, Alfio; Tuveri, Massimiliano; Veneziani, Alessandro 107 2000 Cardiovascular mathematics. Modeling and simulation of the circulatory system. Zbl 1300.92005Formaggia, Luca (ed.); Quarteroni, Alfio (ed.); Veneziani, Alessandro (ed.) 105 2009 Numerical mathematics. Zbl 0913.65002Quarteroni, A.; Sacco, R.; Saleri, F. 100 1998 Numerical mathematics. (Matematica numerica). 2nd ed. Zbl 0943.65001Quarteroni, A.; Sacco, R.; Saleri, F. 98 2000 Robin-Robin domain decomposition methods for the Stokes-Darcy coupling. Zbl 1139.76030Discacciati, Marco; Quarteroni, Alfio; Valli, Alberto 76 2007 Navier-Stokes/Darcy coupling: modeling, analysis, and numerical approximation. Zbl 1172.76050Discacciati, Marco; Quarteroni, Alfio 74 2009 Certified reduced basis approximation for parametrized partial differential equations and applications. Zbl 1273.65148Quarteroni, Alfio; Rozza, Gianluigi; Manzoni, Andrea 73 2011 One-dimensional models for blood flow in arteries. Zbl 1070.76059Formaggia, Luca; Lamponi, Daniele; Quarteroni, Alfio 69 2003 Multiscale modelling of the circulatory system: a preliminary analysis. Zbl 1067.76624Formaggia, Luca; Nobile, Fabio; Quarteroni, Alfio; Veneziani, Alessandro 63 1999 Factorization methods for the numerical approximation of Navier-Stokes equations. Zbl 0976.76044Quarteroni, Alfio; Saleri, Fausto; Veneziani, Alessandro 62 2000 Convergence analysis of a subdomain iterative method for the finite element approximation of the coupling of Stokes and Darcy equations. Zbl 1299.76252Discacciati, Marco; Quarteroni, Alfio 59 2004 Numerical treatment of defective boundary conditions for the Navier-Stokes equations. Zbl 1020.35070Formaggia, L.; Gerbeau, J.-F.; Nobile, F.; Quarteroni, A. 58 2002 An iterative procedure with interface relaxation for domain decomposition methods. Zbl 0678.65082Funaro, Daniele; Quarteroni, Alfio; Zanolli, Paola 58 1988 A relaxation procedure for domain decomposition methods using finite elements. Zbl 0661.65111Marini, L. D.; Quarteroni, A. 55 1989 Splitting methods based on algebraic factorization for fluid-structure interaction. Zbl 1368.74021Badia, Santiago; Quaini, Annalisa; Quarteroni, Alfio 51 2008 Fluid-structure algorithms based on Steklov-Poincaré operators. Zbl 1124.76026Deparis, Simone; Discacciati, Marco; Fourestey, Gilles; Quarteroni, Alfio 51 2006 Numerical analysis of the Navier-Stokes/Darcy coupling. Zbl 1423.35304Badea, Lori; Discacciati, Marco; Quarteroni, Alfio 48 2010 Supremizer stabilization of POD-Galerkin approximation of parametrized steady incompressible Navier-Stokes equations. Zbl 1352.76039Ballarin, Francesco; Manzoni, Andrea; Quarteroni, Alfio; Rozza, Gianluigi 46 2015 Isogeometric analysis and error estimates for high order partial differential equations in fluid dynamics. Zbl 1391.76360Tagliabue, Anna; Dedè, Luca; Quarteroni, Alfio 44 2014 Modular vs. non-modular preconditioners for fluid-structure systems with large added-mass effect. Zbl 1194.74058Badia, Santiago; Quaini, Annalisa; Quarteroni, Alfio 44 2008 Numerical models for differential problems. Translated by Silvia Quarteroni. Translation from the 4th Italian ed. Zbl 1170.65326Quarteroni, Alfio M. 43 2009 Analysis of a domain decomposition method for the coupling of Stokes and Darcy equations. Zbl 1254.76051Discacciati, M.; Quarteroni, A. 39 2003 A semi-implicit approach for fluid-structure interaction based on an algebraic fractional step method. Zbl 1388.74041Quaini, A.; Quarteroni, A. 37 2007 Analysis of a geometrical multiscale model based on the coupling of ODEs and PDEs for blood flow simulations. Zbl 1060.35003Quarteroni, Alfio; Veneziani, Alessandro 37 2003 Numerical solution of parametrized Navier-Stokes equations by reduced basis methods. Zbl 1178.76238Quarteroni, Alfio; Rozza, Gianluigi 36 2007 On the coupling of 1D and 3D diffusion-reaction equations. Application to tissue perfusion problems. Zbl 1359.35200D’Angelo, C.; Quarteroni, A. 35 2008 Parallel algorithms for fluid-structure interaction problems in haemodynamics. Zbl 1417.92008Crosetto, Paolo; Deparis, Simone; Fourestey, Gilles; Quarteroni, Alfio 34 2011 Reduced basis method for parametrized elliptic optimal control problems. Zbl 1280.49046Negri, Federico; Rozza, Gianluigi; Manzoni, Andrea; Quarteroni, Alfio 31 2013 Model order reduction in fluid dynamics: challenges and perspectives. Zbl 1395.76058Lassila, Toni; Manzoni, Andrea; Quarteroni, Alfio; Rozza, Gianluigi 29 2014 Coupling Biot and Navier-Stokes equations for modelling fluid-poroelastic media interaction. Zbl 1391.74234Badia, Santiago; Quaini, Annalisa; Quarteroni, Alfio 29 2009 Spectral and pseudo-spectral approximations of the Navier-Stokes equations. Zbl 0503.76035Maday, Y.; Quarteroni, A. 28 1982 Comparison between reduced basis and stochastic collocation methods for elliptic problems. Zbl 1301.65007Chen, Peng; Quarteroni, Alfio; Rozza, Gianluigi 27 2014 A weighted reduced basis method for elliptic partial differential equations with random input data. Zbl 1288.65007Chen, Peng; Quarteroni, Alfio; Rozza, Gianluigi 27 2013 Legendre and Chebyshev spectral approximations of Burgers’ equation. Zbl 0452.41007Maday, Yvon; Quarteroni, Alfio 27 1981 A multiscale Darcy-Brinkman model for fluid flow in fractured porous media. Zbl 1305.76109Lesinigo, Matteo; D’Angelo, Carlo; Quarteroni, Alfio 26 2011 Isogeometric analysis of high order partial differential equations on surfaces. Zbl 1425.65145Bartezzaghi, Andrea; Dedè, Luca; Quarteroni, Alfio 25 2015 An active strain electromechanical model for cardiac tissue. Zbl 1242.92016Nobile, F.; Quarteroni, A.; Ruiz-Baier, R. 25 2012 Fluid-structure interaction simulation of aortic blood flow. Zbl 05909596Crosetto, Paolo; Reymond, Philippe; Deparis, Simone; Kontaxakis, Dimitrios; Stergiopulos, Nikolaos; Quarteroni, Alfio 25 2011 Optimal control and shape optimization of aorto-coronaric bypass anastomoses. Zbl 1063.49029Quarteroni, Alfio; Rozza, Gianluigi 25 2003 Theory and application of Steklov-Poincaré operators for boundary-value problems. Zbl 0723.65098Quarteroni, A.; Valli, A. 25 1991 Weighted reduced basis method for stochastic optimal control problems with elliptic PDE constraint. Zbl 1309.35182Chen, Peng; Quarteroni, Alfio 24 2014 A reduced basis hybrid method for the coupling of parametrized domains represented by fluidic networks. Zbl 1253.76139Iapichino, Laura; Quarteroni, Alfio; Rozza, Gianluigi 24 2012 Advanced numerical approximation of nonlinear hyperbolic equations. Lectures given at the 2nd session of the Centro Internazionale Matematico Estivo (C. I. M. E.) held in Cetraro, Italy, June 23–28, 1997. Zbl 0904.00047Quarteroni, Alfio (ed.); Cockburn, B.; Johnson, C.; Shu, C.-W.; Tadmor, E. 24 1998 Error analysis for spectral approximation of the Korteweg-de Vries equation. Zbl 0647.65082Maday, Y.; Quarteroni, A. 24 1988 Electromechanical coupling in cardiac dynamics: the active strain approach. Zbl 1419.74174Ambrosi, D.; Arioli, G.; Nobile, F.; Quarteroni, A. 23 2011 Analysis of a geometrical multiscale blood flow model based on the coupling of ODEs and hyperbolic PDEs. Zbl 1085.35095Fernández, Miguel Ángel; Milisic, Vuk; Quarteroni, Alfio 23 2005 Coupling between lumped and distributed models for blood flow problems. Zbl 1097.76615Quarteroni, Alfio; Ragni, Stefania; Veneziani, Alessandro 23 2001 Domain decomposition preconditioners for the spectral collocation method. Zbl 0661.65121Quarteroni, Alfio; Sacchi-Landriani, Giovanni 23 1988 Preconditioned minimal residual methods for Chebyshev spectral calculations. Zbl 0615.65118Canuto, Claudio; Quarteroni, Alfio 22 1985 A rescaled localized radial basis function interpolation on non-Cartesian and nonconforming grids. Zbl 1312.41006Deparis, Simone; Forti, Davide; Quarteroni, Alfio 21 2014 Accurate and efficient evaluation of failure probability for partial different equations with random input data. Zbl 1286.65156Chen, Peng; Quarteroni, Alfio 21 2013 Analysis of the Yosida method for the incompressible Navier-Stokes equations. Zbl 0930.35127Quarteroni, Alfio; Saleri, Fausto; Veneziani, Alessandro 21 1999 Fourier spectral methods for pseudo-parabolic equations. Zbl 0621.65120Quarteroni, Alfio 21 1987 Spectral and pseudo-spectral methods for parabolic problems with non periodic boundary conditions. Zbl 0485.65078Canuto, C.; Quarteroni, A. 21 1981 Thermodynamically consistent orthotropic activation model capturing ventricular systolic wall thickening in cardiac electromechanics. Zbl 1406.74503Rossi, Simone; Lassila, Toni; Ruiz-Baier, Ricardo; Sequeira, Adélia; Quarteroni, Alfio 20 2014 Numerical models for differential problems. Translated from the 5th Italian edition by Silvia Quarteroni. 2nd ed. Zbl 1285.65054Quarteroni, Alfio 20 2014 Reduced order methods for modeling and computational reduction. Zbl 1280.65004Quarteroni, Alfio (ed.); Rozza, Gianluigi (ed.) 20 2014 Mathematical and numerical modeling of solute dynamics in blood flow and arterial walls. Zbl 1022.76059Quarteroni, Alfio; Veneziani, Alessandro; Zunino, Paolo 20 2001 On the coupling of hyperbolic and parabolic systems: Analytical and numerical approach. Zbl 0686.65084Gastaldi, Fabio; Quarteroni, Alfio 20 1989 An implicit/explicit spectral method for Burgers’ equation. Zbl 0691.65081Bressan, N.; Quarteroni, A. 19 1986 Error estimates for spectral and pseudospectral approximations of hyperbolic equations. Zbl 0508.65054Canuto, C.; Quarteroni, A. 19 1982 Facsi: a block parallel preconditioner for fluid-structure interaction in hemodynamics. Zbl 1373.74036Deparis, Simone; Forti, Davide; Grandperrin, Gwenol; Quarteroni, Alfio 18 2016 Multilevel and weighted reduced basis method for stochastic optimal control problems constrained by Stokes equations. Zbl 1344.93109Chen, Peng; Quarteroni, Alfio; Rozza, Gianluigi 18 2016 Non-conforming high order approximations of the elastodynamics equation. Zbl 1243.74010Antonietti, Paola F.; Mazzieri, Ilario; Quarteroni, Alfio; Rapetti, Francesca 18 2012 Coupling of free surface and groundwater flows. Zbl 1035.76051Miglio, Edie; Quarteroni, Alfio; Saleri, Fausto 18 2003 Variational methods in the theoretical analysis of spectral approximations. Zbl 0539.65080Canuto, Claudio; Quarteroni, Alfio 18 1984 Multiscale homogenization for fluid and drug transport in vascularized malignant tissues. Zbl 1307.92062Penta, R.; Ambrosi, D.; Quarteroni, A. 17 2015 Isogeometric analysis for second order partial differential equations on surfaces. Zbl 1425.65156Dedè, Luca; Quarteroni, Alfio 16 2015 Optimal control and numerical adaptivity for advection-diffusion equations. Zbl 1075.49014Dede, Luca; Quarteroni, Alfio 16 2005 Finite element preconditioning for Legendre spectral collocation approximations to elliptic equations and systems. Zbl 0753.65087Quarteroni, Alfio; Zampieri, Elena 16 1992 Reduced basis methods for uncertainty quantification. Zbl 1400.65010Chen, Peng; Quarteroni, Alfio; Rozza, Gianluigi 15 2017 Isogeometric numerical dispersion analysis for two-dimensional elastic wave propagation. Zbl 1423.74094Dedè, Luca; Jäggli, Christoph; Quarteroni, Alfio 15 2015 Reduced basis method for linear elasticity problems with many parameters. Zbl 1194.74445Milani, Roberto; Quarteroni, Alfio; Rozza, Gianluigi 15 2008 Heterogeneous coupling by virtual control methods. Zbl 1002.65133Gervasio, P.; Lions, J.-L.; Quarteroni, A. 15 2001 Finite element approximation of quasi-3D shallow water equations. Zbl 0958.76046Miglio, Edie; Quarteroni, Alfio; Saleri, Fausto 15 1999 Combined finite element and spectral approximation of the Navier-Stokes equations. Zbl 0614.76021Canuto, Claudio; Maday, Yvon; Quarteroni, Alfio 15 1984 Some results of Bernstein and Jackson type for polynomial approximation in \(L^ p\)-spaces. Zbl 0568.41006Quarteroni, Alfio 15 1984 Comparisons between reduced order models and full 3D models for fluid-structure interaction problems in haemodynamics. Zbl 1293.92008Colciago, C. M.; Deparis, S.; Quarteroni, A. 14 2014 On the physical consistency between three-dimensional and one-dimensional models in haemodynamics. Zbl 1377.76042Formaggia, Luca; Quarteroni, Alfio; Vergara, Christian 14 2013 Stochastic optimal Robin boundary control problems of advection-dominated elliptic equations. Zbl 1281.49015Chen, Peng; Quarteroni, Alfio; Rozza, Gianluigi 14 2013 Generalized Galerkin approximations of elastic waves with absorbing boundary conditions. Zbl 0964.74079Quarteroni, A.; Tagliani, A.; Zampieri, E. 14 1998 Domain decomposition methods for systems of conservation laws: Spectral collocation approximations. Zbl 0711.65082Quarteroni, Alfio 14 1990 A new algorithm for high-dimensional uncertainty quantification based on dimension-adaptive sparse grid approximation and reduced basis methods. Zbl 1349.65683Chen, Peng; Quarteroni, Alfio 13 2015 Mathematical modelling of active contraction in isolated cardiomyocytes. Zbl 1304.92054Ruiz-Baier, Ricardo; Gizzi, Alessio; Rossi, Simone; Cherubini, Christian; Laadhari, Aymen; Filippi, Simonetta; Quarteroni, Alfio 13 2014 A weighted empirical interpolation method: a priori convergence analysis and applications. Zbl 1304.65097Chen, Peng; Quarteroni, Alfio; Rozza, Gianluigi 13 2014 Finite-element preconditioning of G-NI spectral methods. Zbl 1223.65089Canuto, Claudio; Gervasio, Paola; Quarteroni, Alfio 13 2010 Mathematical modelling of the human cardiovascular system. Data, numerical approximation, clinical applications. Zbl 1411.92003Quarteroni, Alfio; Dede’, Luca; Manzoni, Andrea; Vergara, Christian 4 2019 A monolithic algorithm for the simulation of cardiac electromechanics in the human left ventricle. Zbl 1442.92006Gerbi, Antonello; Dedè, Luca; Quarteroni, Alfio 2 2019 Multi space reduced basis preconditioners for parametrized Stokes equations. Zbl 1442.65357Dal Santo, Niccolo; Deparis, S.; Manzoni, A.; Quarteroni, A. 1 2019 An algebraic least squares reduced basis method for the solution of nonaffinely parametrized Stokes equations. Zbl 1440.76055Dal Santo, Niccolo; Deparis, S.; Manzoni, A.; Quarteroni, A. 1 2019 A saddle point approach to an optimal boundary control problem for steady Navier-Stokes equations. Zbl 1434.49021Manzoni, Andrea; Quarteroni, Alfio; Salsa, Sandro 1 2019 The INTERNODES method for non-conforming discretizations of PDEs. Zbl 1449.65344Gervasio, Paola; Quarteroni, Alfio 1 2019 Application of the rosenbrock methods to the solution of unsteady 3D incompressible Navier-Stokes equations. Zbl 1411.76059Deparis, Simone; Deville, Michel O.; Menghini, Filippo; Pegolotti, Luca; Quarteroni, Alfio 1 2019 Numerical models for differential problems. 3rd edition. Zbl 1436.65003Quarteroni, Alfio 12 2018 A high-order discontinuous Galerkin approximation to ordinary differential equations with applications to elastodynamics. Zbl 06983860Antonietti, Paola F.; Mazzieri, Ilario; Dal Santo, Niccolò; Quarteroni, Alfio 6 2018 Multi space reduced basis preconditioners for large-scale parametrized pdes. Zbl 06856497Santo, Niccolò Dal; Deparis, Simone; Manzoni, Andrea; Quarteroni, Alfio 3 2018 Numerical approximation of parametrized problems in cardiac electrophysiology by a local reduced basis method. Zbl 1440.92003Pagani, Stefano; Manzoni, Andrea; Quarteroni, Alfio 2 2018 Analysis of the INTERNODES method for non-conforming discretizations of elliptic equations. Zbl 1440.65203Gervasio, Paola; Quarteroni, Alfio 2 2018 Numerical modeling of seismic waves by discontinuous spectral element methods. Zbl 07007336Antonietti, Paola F.; Ferroni, Alberto; Mazzieri, Ilario; Paolucci, Roberto; Quarteroni, Alfio; Smerzini, Chiara; Stupazzini, Marco 2 2018 The role of statistics in the era of big data: a computational scientist’ perspective. Zbl 06892167Quarteroni, Alfio 2 2018 Isogeometric analysis of a phase field model for Darcy flows with discontinuous data. Zbl 1397.65116Dedè, Luca; Quarteroni, Alfio 1 2018 Reduced basis methods for uncertainty quantification. Zbl 1400.65010Chen, Peng; Quarteroni, Alfio; Rozza, Gianluigi 15 2017 The cardiovascular system: mathematical modelling, numerical algorithms and clinical applications. Zbl 1376.92016Quarteroni, A.; Manzoni, A.; Vergara, C. 8 2017 Isogeometric analysis and proper orthogonal decomposition for the acoustic wave equation. Zbl 1381.65086Zhu, Shengfeng; Dedè, Luca; Quarteroni, Alfio 5 2017 Integrated heart – coupling multiscale and multiphysics models for the simulation of the cardiac function. Zbl 1439.74208Quarteroni, Alfio; Lassila, Toni; Rossi, Simone; Ruiz-Baier, Ricardo 4 2017 \(hp\)-version discontinuous Galerkin approximations of the elastodynamics equation. Zbl 1388.74090Antonietti, Paola F.; Ferroni, Alberto; Mazzieri, Ilario; Quarteroni, Alfio 4 2017 Isogeometric analysis and proper orthogonal decomposition for parabolic problems. Zbl 1380.65295Zhu, Shengfeng; Dedè, Luca; Quarteroni, Alfio 4 2017 Efficient state/parameter estimation in nonlinear unsteady PDEs by a reduced basis ensemble Kalman filter. Zbl 1398.65280Pagani, Stefano; Manzoni, Andrea; Quarteroni, Alfio 2 2017 A parallel algorithm for the solution of large-scale nonconforming fluid-structure interaction problems in hemodynamics. Zbl 1399.65237Forti, Davide; Quarteroni, Alfio; Deparis, Simone 2 2017 Isogeometric approximation of cardiac electrophysiology models on surfaces: an accuracy study with application to the human left atrium. Zbl 1439.76090Patelli, Alessandro S.; Dedè, Luca; Lassila, Toni; Bartezzaghi, Andrea; Quarteroni, Alfio 1 2017 Reduced basis methods for partial differential equations. An introduction. Zbl 1337.65113Quarteroni, Alfio; Manzoni, Andrea; Negri, Federico 140 2016 Facsi: a block parallel preconditioner for fluid-structure interaction in hemodynamics. Zbl 1373.74036Deparis, Simone; Forti, Davide; Grandperrin, Gwenol; Quarteroni, Alfio 18 2016 Multilevel and weighted reduced basis method for stochastic optimal control problems constrained by Stokes equations. Zbl 1344.93109Chen, Peng; Quarteroni, Alfio; Rozza, Gianluigi 18 2016 Geometric multiscale modeling of the cardiovascular system, between theory and practice. Zbl 1423.76528Quarteroni, A.; Veneziani, A.; Vergara, C. 11 2016 Fast simulations of patient-specific haemodynamics of coronary artery bypass grafts based on a POD-Galerkin method and a vascular shape parametrization. Zbl 1349.76173Ballarin, Francesco; Faggiano, Elena; Ippolito, Sonia; Manzoni, Andrea; Quarteroni, Alfio; Rozza, Gianluigi; Scrofani, Roberto 11 2016 Stability analysis of discontinuous Galerkin approximations to the elastodynamics problem. Zbl 1383.74082Antonietti, Paola F.; Ayuso de Dios, Blanca; Mazzieri, Ilario; Quarteroni, Alfio 10 2016 INTERNODES: an accurate interpolation-based method for coupling the Galerkin solutions of PDEs on subdomains featuring non-conforming interfaces. Zbl 1390.65142Deparis, Simone; Forti, Davide; Gervasio, Paola; Quarteroni, Alfio 9 2016 High order discontinuous Galerkin methods on simplicial elements for the elastodynamics equation. Zbl 1398.74291Antonietti, Paola F.; Marcati, Carlo; Mazzieri, Ilario; Quarteroni, Alfio 9 2016 Parameter estimates for the relaxed dimensional factorization preconditioner and application to hemodynamics. Zbl 1423.76212Benzi, Michele; Deparis, Simone; Grandperrin, Gwenol; Quarteroni, Alfio 8 2016 A discontinuous Galerkin reduced basis element method for elliptic problems. Zbl 1343.65132Antonietti, Paola F.; Pacciarini, Paolo; Quarteroni, Alfio 8 2016 The interface control domain decomposition method for Stokes-Darcy coupling. Zbl 1337.49056Discacciati, Marco; Gervasio, Paola; Giacomini, Alessandro; Quarteroni, Alfio 7 2016 An online intrinsic stabilization strategy for the reduced basis approximation of parametrized advection-dominated problems. Zbl 1353.65093Maday, Yvon; Manzoni, Andrea; Quarteroni, Alfio 5 2016 A fluid-structure interaction algorithm using radial basis function interpolation between non-conforming interfaces. Zbl 1356.74196Deparis, Simone; Forti, Davide; Quarteroni, Alfio 4 2016 A coupled 3D-1D numerical monodomain solver for cardiac electrical activation in the myocardium with detailed Purkinje network. Zbl 1352.92006Vergara, Christian; Lange, Matthias; Palamara, Simone; Lassila, Toni; Frangi, Alejandro F.; Quarteroni, Alfio 4 2016 A time-parallel framework for coupling finite element and lattice Boltzmann methods. Zbl 1336.65161Astorino, Matteo; Chouly, Franz; Quarteroni, Alfio 3 2016 Spectral based discontinuous Galerkin reduced basis element method for parametrized Stokes problems. Zbl 1365.76125Pacciarini, Paolo; Gervasio, Paola; Quarteroni, Alfio 1 2016 Nitsche’s method for parabolic partial differential equations with mixed time varying boundary conditions. Zbl 1382.65327Tagliabue, Anna; Dedè, Luca; Quarteroni, Alfio 1 2016 Numerical modeling for differential problems. 6th edition. Zbl 1342.65171Quarteroni, Alfio 1 2016 Supremizer stabilization of POD-Galerkin approximation of parametrized steady incompressible Navier-Stokes equations. Zbl 1352.76039Ballarin, Francesco; Manzoni, Andrea; Quarteroni, Alfio; Rozza, Gianluigi 46 2015 Isogeometric analysis of high order partial differential equations on surfaces. Zbl 1425.65145Bartezzaghi, Andrea; Dedè, Luca; Quarteroni, Alfio 25 2015 Multiscale homogenization for fluid and drug transport in vascularized malignant tissues. Zbl 1307.92062Penta, R.; Ambrosi, D.; Quarteroni, A. 17 2015 Isogeometric analysis for second order partial differential equations on surfaces. Zbl 1425.65156Dedè, Luca; Quarteroni, Alfio 16 2015 Isogeometric numerical dispersion analysis for two-dimensional elastic wave propagation. Zbl 1423.74094Dedè, Luca; Jäggli, Christoph; Quarteroni, Alfio 15 2015 A new algorithm for high-dimensional uncertainty quantification based on dimension-adaptive sparse grid approximation and reduced basis methods. Zbl 1349.65683Chen, Peng; Quarteroni, Alfio 13 2015 Reduced basis techniques for nonlinear conservation laws. Zbl 1316.65079Taddei, T.; Perotto, S.; Quarteroni, A. 11 2015 Well-posedness, regularity, and convergence analysis of the finite element approximation of a generalized Robin boundary value problem. Zbl 1326.65161Kashiwabara, Takahito; Colciago, Claudia Maria; Dedè, Luca; Quarteroni, Alfio 7 2015 Solvability analysis and numerical approximation of linearized cardiac electromechanics. Zbl 1309.74049Andreianov, Boris; Bendahmane, Mostafa; Quarteroni, Alfio; Ruiz-Baier, Ricardo 6 2015 Finite element and finite volume-element simulation of pseudo-ECGs and cardiac alternans. Zbl 1309.65111Dupraz, Marie; Filippi, Simonetta; Gizzi, Alessio; Quarteroni, Alfio; Ruiz-Baier, Ricardo 2 2015 Isogeometric analysis and error estimates for high order partial differential equations in fluid dynamics. Zbl 1391.76360Tagliabue, Anna; Dedè, Luca; Quarteroni, Alfio 44 2014 Model order reduction in fluid dynamics: challenges and perspectives. Zbl 1395.76058Lassila, Toni; Manzoni, Andrea; Quarteroni, Alfio; Rozza, Gianluigi 29 2014 Comparison between reduced basis and stochastic collocation methods for elliptic problems. Zbl 1301.65007Chen, Peng; Quarteroni, Alfio; Rozza, Gianluigi 27 2014 Weighted reduced basis method for stochastic optimal control problems with elliptic PDE constraint. Zbl 1309.35182Chen, Peng; Quarteroni, Alfio 24 2014 A rescaled localized radial basis function interpolation on non-Cartesian and nonconforming grids. Zbl 1312.41006Deparis, Simone; Forti, Davide; Quarteroni, Alfio 21 2014 Thermodynamically consistent orthotropic activation model capturing ventricular systolic wall thickening in cardiac electromechanics. Zbl 1406.74503Rossi, Simone; Lassila, Toni; Ruiz-Baier, Ricardo; Sequeira, Adélia; Quarteroni, Alfio 20 2014 Numerical models for differential problems. Translated from the 5th Italian edition by Silvia Quarteroni. 2nd ed. Zbl 1285.65054Quarteroni, Alfio 20 2014 Reduced order methods for modeling and computational reduction. Zbl 1280.65004Quarteroni, Alfio (ed.); Rozza, Gianluigi (ed.) 20 2014 Comparisons between reduced order models and full 3D models for fluid-structure interaction problems in haemodynamics. Zbl 1293.92008Colciago, C. M.; Deparis, S.; Quarteroni, A. 14 2014 Mathematical modelling of active contraction in isolated cardiomyocytes. Zbl 1304.92054Ruiz-Baier, Ricardo; Gizzi, Alessio; Rossi, Simone; Cherubini, Christian; Laadhari, Aymen; Filippi, Simonetta; Quarteroni, Alfio 13 2014 A weighted empirical interpolation method: a priori convergence analysis and applications. Zbl 1304.65097Chen, Peng; Quarteroni, Alfio; Rozza, Gianluigi 13 2014 Parallel preconditioners for the unsteady Navier-Stokes equations and applications to hemodynamics simulations. Zbl 1391.76887Deparis, Simone; Grandperrin, Gwenol; Quarteroni, Alfio 12 2014 An orthotropic active-strain model for the myocardium mechanics and its numerical approximation. Zbl 1406.74502Pezzuto, Simone; Ambrosi, Davide; Quarteroni, Alfio 7 2014 Scientific computing with MATLAB and Octave. 4th ed. Zbl 1306.65001Quarteroni, Alfio; Saleri, Fausto; Gervasio, Paola 5 2014 High order space-time discretization for elastic wave propagation problems. Zbl 1417.74012Antonietti, Paola F.; Mazzieri, Ilario; Quarteroni, Alfio; Rapetti, Francesca 4 2014 Modeling the heart and the circulatory system. Zbl 1307.92010Quarteroni, Alfio (ed.) 3 2014 Reduced basis method for parametrized elliptic optimal control problems. Zbl 1280.49046Negri, Federico; Rozza, Gianluigi; Manzoni, Andrea; Quarteroni, Alfio 31 2013 A weighted reduced basis method for elliptic partial differential equations with random input data. Zbl 1288.65007Chen, Peng; Quarteroni, Alfio; Rozza, Gianluigi 27 2013 Accurate and efficient evaluation of failure probability for partial different equations with random input data. Zbl 1286.65156Chen, Peng; Quarteroni, Alfio 21 2013 On the physical consistency between three-dimensional and one-dimensional models in haemodynamics. Zbl 1377.76042Formaggia, Luca; Quarteroni, Alfio; Vergara, Christian 14 2013 Stochastic optimal Robin boundary control problems of advection-dominated elliptic equations. Zbl 1281.49015Chen, Peng; Quarteroni, Alfio; Rozza, Gianluigi 14 2013 Asymptotic-numerical derivation of the Robin type coupling conditions for the macroscopic pressure at a reservoir-capillaries interface. Zbl 1270.35062D’Angelo, Carlo; Panasenko, Grigory; Quarteroni, Alfio 8 2013 Fully Eulerian finite element approximation of a fluid-structure interaction problem in cardiac cells. Zbl 1352.74388Laadhari, A.; Ruiz-Baier, R.; Quarteroni, A. 7 2013 Implicit coupling of one-dimensional and three-dimensional blood flow models with compliant vessels. Zbl 1310.92017Malossi, A. Cristiano I.; Blanco, Pablo J.; Crosetto, Paolo; Deparis, Simone; Quarteroni, Alfio 7 2013 The interface control domain decomposition (ICDD) method for elliptic problems. Zbl 1284.65180Discacciati, Marco; Gervasio, Paola; Quarteroni, Alfio 7 2013 Boundary control and shape optimization for the robust design of bypass anastomoses under uncertainty. Zbl 1402.92246Lassila, Toni; Manzoni, Andrea; Quarteroni, Alfio; Rozza, Gianluigi 7 2013 Generalized reduced basis methods and \(n\)-width estimates for the approximation of the solution manifold of parametric PDEs. Zbl 1347.41033Lassila, Toni; Manzoni, Andrea; Quarteroni, Alfio; Rozza, Gianluigi 6 2013 Convergence of a stabilized discontinuous Galerkin method for incompressible nonlinear elasticity. Zbl 1271.74030Baroli, Davide; Quarteroni, Alfio; Ruiz-Baier, Ricardo 5 2013 Numerical approximation of internal discontinuity interface problems. Zbl 1281.65146Discacciati, Marco; Quarteroni, Alfio; Quinodoz, Samuel 4 2013 Numerical simulation of orbitally shaken viscous fluids with free surface. Zbl 1430.76113Discacciati, Marco; Hacker, David; Quarteroni, Alfio; Quinodoz, Samuel; Tissot, Stéphanie; Wurm, Florian M. 2 2013 Free form deformation techniques applied to 3D shape optimization problems. Zbl 1329.49091Rozza, Gianluigi; Koshakji, Anwar; Quarteroni, Alfio 2 2013 Radial basis functions for inter-grid interpolation and mesh motion in FSI problems. Zbl 1352.74475Lombardi, M.; Parolini, N.; Quarteroni, A. 1 2013 Generalized reduced basis methods and \(n\)-width estimates for the approximation of the solution manifold of parametric PDEs. Zbl 1273.35024Lassila, Toni; Manzoni, Andrea; Quarteroni, Alfio; Rozza, Gianluigi 1 2013 An active strain electromechanical model for cardiac tissue. Zbl 1242.92016Nobile, F.; Quarteroni, A.; Ruiz-Baier, R. 25 2012 A reduced basis hybrid method for the coupling of parametrized domains represented by fluidic networks. Zbl 1253.76139Iapichino, Laura; Quarteroni, Alfio; Rozza, Gianluigi 24 2012 Non-conforming high order approximations of the elastodynamics equation. Zbl 1243.74010Antonietti, Paola F.; Mazzieri, Ilario; Quarteroni, Alfio; Rapetti, Francesca 18 2012 Shape optimization for viscous flows by reduced basis methods and free-form deformation. Zbl 1412.76031Manzoni, Andrea; Quarteroni, Alfio; Rozza, Gianluigi 11 2012 Computational reduction for parametrized PDEs: strategies and applications. Zbl 1432.65171Manzoni, Andrea; Quarteroni, Alfio; Rozza, Gianluigi 9 2012 A reduced basis model with parametric coupling for fluid-structure interaction problems. Zbl 1390.74053Lassila, Toni; Quarteroni, Alfio; Rozza, Gianluigi 8 2012 Heterogeneous mathematical models in fluid dynamics and associated solution algorithms. Zbl 1426.76527Discacciati, Marco; Gervasio, Paola; Quarteroni, Alfio 6 2012 A modular lattice Boltzmann solver for GPU computing. Zbl 1260.65117Astorino, M.; Becerra-Sagredo, J.; Quarteroni, A. 1 2012 High order methods for the approximation of the incompressible Navier-Stokes equations in a moving domain. Zbl 1243.76020Pena, Gonçalo; Prud’homme, Christophe; Quarteroni, Alfio 1 2012 Certified reduced basis approximation for parametrized partial differential equations and applications. Zbl 1273.65148Quarteroni, Alfio; Rozza, Gianluigi; Manzoni, Andrea 73 2011 Parallel algorithms for fluid-structure interaction problems in haemodynamics. Zbl 1417.92008Crosetto, Paolo; Deparis, Simone; Fourestey, Gilles; Quarteroni, Alfio 34 2011 A multiscale Darcy-Brinkman model for fluid flow in fractured porous media. Zbl 1305.76109Lesinigo, Matteo; D’Angelo, Carlo; Quarteroni, Alfio 26 2011 Fluid-structure interaction simulation of aortic blood flow. Zbl 05909596Crosetto, Paolo; Reymond, Philippe; Deparis, Simone; Kontaxakis, Dimitrios; Stergiopulos, Nikolaos; Quarteroni, Alfio 25 2011 Electromechanical coupling in cardiac dynamics: the active strain approach. Zbl 1419.74174Ambrosi, D.; Arioli, G.; Nobile, F.; Quarteroni, A. 23 2011 Analysis of a finite volume element method for the Stokes problem. Zbl 1230.65130Quarteroni, Alfio; Ruiz-Baier, Ricardo 11 2011 ...and 173 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 7,707 Authors 129 Quarteroni, Alfio M. 68 Guo, Ben-Yu 62 Bhrawy, Ali Hassan 60 Dehghan Takht Fooladi, Mehdi 50 Rozza, Gianluigi 46 Maday, Yvon 45 Doha, Eid H. 36 Motsa, Sandile Sydney 31 Shen, Jie 30 Gatica, Gabriel N. 30 Heinrichs, Wilhelm 29 Ruiz-Baier, Ricardo 28 Abd-Elhameed, Waleed Mohamed 28 Pavarino, Luca Franco 26 Dede, Luca 26 Ma, Heping 26 Wang, Lilian 25 Canuto, Claudio 25 Hesthaven, Jan S. 25 Kopriva, David Alan 25 Manzoni, Andrea 25 Wang, Zhongqing 23 Băleanu, Dumitru I. 23 Patera, Anthony T. 22 Bernardi, Christine 22 Razzaghi, Mohsen 21 Deparis, Simone 21 Funaro, Daniele 21 Nobile, Fabio 20 Chen, Yanping 20 Gunzburger, Max D. 20 Hou, Yanren 20 Karniadakis, George Em 20 Veneziani, Alessandro 19 Houzeaux, Guillaume 19 Oyarzúa, Ricardo 19 Sibanda, Precious 18 Formaggia, Luca 17 Codina, Ramon 17 Gervasio, Paola 17 Hughes, Thomas J. 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Series B 7 SIAM Journal on Matrix Analysis and Applications 7 SIAM Review ...and 298 more Serials all top 5 Cited in 50 Fields 3,794 Numerical analysis (65-XX) 2,230 Fluid mechanics (76-XX) 1,843 Partial differential equations (35-XX) 699 Mechanics of deformable solids (74-XX) 432 Biology and other natural sciences (92-XX) 319 Ordinary differential equations (34-XX) 244 Calculus of variations and optimal control; optimization (49-XX) 191 Integral equations (45-XX) 167 Classical thermodynamics, heat transfer (80-XX) 156 Approximations and expansions (41-XX) 119 Probability theory and stochastic processes (60-XX) 117 Geophysics (86-XX) 111 Statistical mechanics, structure of matter (82-XX) 110 Optics, electromagnetic theory (78-XX) 95 Systems theory; control (93-XX) 90 Dynamical systems and ergodic theory (37-XX) 86 Operations research, mathematical programming (90-XX) 80 Special functions (33-XX) 80 Statistics (62-XX) 71 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 63 Real functions (26-XX) 63 Harmonic analysis on Euclidean spaces (42-XX) 57 Computer science (68-XX) 45 Operator theory (47-XX) 44 Quantum theory (81-XX) 38 Linear and multilinear algebra; matrix theory (15-XX) 25 Mechanics of particles and systems (70-XX) 19 Functional analysis (46-XX) 17 Astronomy and astrophysics (85-XX) 15 Relativity and gravitational theory (83-XX) 13 Potential theory (31-XX) 12 Information and communication theory, circuits (94-XX) 11 General and overarching topics; collections (00-XX) 9 Global analysis, analysis on manifolds (58-XX) 8 Difference and functional equations (39-XX) 6 Combinatorics (05-XX) 6 Number theory (11-XX) 5 Functions of a complex variable (30-XX) 4 History and biography (01-XX) 3 Algebraic geometry (14-XX) 3 Integral transforms, operational calculus (44-XX) 2 Measure and integration (28-XX) 2 Sequences, series, summability (40-XX) 2 Differential geometry (53-XX) 1 Mathematical logic and foundations (03-XX) 1 Category theory; homological algebra (18-XX) 1 Geometry (51-XX) 1 Convex and discrete geometry (52-XX) 1 1 Mathematics education (97-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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